Phase diagram of a tetrahedral patchy particle model for different interaction ranges

Romano, Flavio; Sanz, Eduardo; Sciortino, Francesco

doi:10.1063/1.3393777

Cited by 127 publications

(185 citation statements)

References 42 publications

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“…For narrow patch width, the four-patch phase diagram closely resembles the standard phase diagrams with a triple point below which the liquid state ceases to exist 19 . Unexpectedly, for wider patches the diamond crystal disappears from the phase diagram and a region in which the liquid is stable down to vanishing T opens up at intermediate ρ, in agreement with a numerical study of DNA-functionalized colloids 12,20 .…”

mentioning

confidence: 79%

Liquids more stable than crystals in particles with limited valence and flexible bonds

2013

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All liquids (except helium owing to quantum effects) crystallize at low temperatures, forming ordered structures. The competition between disorder, which stabilizes the liquid phase, and energy, which leads to a preference for the crystalline structure, inevitably favours the crystal when the temperature is lowered and entropy becomes progressively less relevant. The liquid state survives at low temperatures only as a glass, an out-of-equilibrium arrested state of matter. This textbook description holds inevitably for atomic and molecular systems, where particle interactions are set by quantum-mechanical laws. The question remains whether it holds for colloidal particles, where interparticle interactions are usually short-ranged and tunable. Here we show that for patchy colloids with limited valence 1 , conditions can be found for which the liquid phase is stable even in the zero-temperature limit. Our results offer fresh cues for understanding the stability of gels 2 and the glass-forming ability of molecular network glasses 3,4 .The ability to control the selectivity and angular flexibility of interparticle interactions 5 makes it possible to provide valence to colloids. This can be done by means of chemical [6][7][8] or physical 9 patterning of the colloid surface, that is, locally changing either its chemical properties (for example, hydrophobicity), or the physical properties (for example, roughness). Exploiting valence offers enormous possibilities, some of which have been addressed in recent years, theoretically 10 , numerically 4,11,12 and experimentally 2,7,13,14 . As colloidal interactions are typically shortranged, valence provides an implicit quantization of the particle energy, which becomes essentially proportional to the (limited) number of formed bonds. In an optimal arrangement, all particles bind with their maximum number of neighbours and the system is in its lowest possible (ground) energy state. Typically, such an optimal arrangement is spatially ordered, defining the most stable crystal phase(s).In principle, when the density is not too high, it is possible to imagine disordered arrangements in which all particles are fully bonded, with exactly the same energy as the crystal. Such a state, which was recently shown to be stable in a model system for DNA-functionalized colloids 12 , is a liquid: a fluid, disordered phase at temperatures below the critical temperature. Under this unconventional condition, the stability of the system becomes controlled by its entropy, a case reminiscent of (purely entropydriven) hard-sphere particles. In this study we demonstrate that the flexibility of the bonds (encoded in the angular patch width)-a tunable quantity in the design of patchy colloidal particles-is the key element in controlling the entropy of the liquid as compared with that of the crystal. Large binding angles combined with limited valence give rise to a thermodynamically stable, fully bonded liquid phase.Department of Physics, Sapienza, Universitá di Roma, Piazzale Aldo Moro 2, I-00185, Roma,...

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confidence: 79%

Liquids more stable than crystals in particles with limited valence and flexible bonds

2013

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“…The global enthalpy minimum for this pressure value corresponds to, as previously reported in [12,5,8], a bcc-like structure that consists of two interpenetrating, but virtually non-interacting diamond lattices. This structure emerges in two different, but closely related versions: the particles of one diamond sublattice can be located exactly in the centers of the voids of the six-particle rings making up the other diamond sublattice ("b" in Figure 1) or the positions of the particles in each sublattice can be slightly shifted against each other ("a" in Figure 1).…”

Section: Structural Variations Along Isobarsmentioning

confidence: 99%

“…Before we start the discussion of structural variations along two selected isobars, we mention two structures, that have raised quite some interest in the literature [12,7,5], namely diamond cubic and diamond hexagonal phases (especially the former, which has potential use in the fabrication of materials with photonic band gaps [22]). In our calculations, these structures appear as corresponding to low-lying minima on the enthalpy landscape for very low pressure values, but as discussed in [5], are never stable for the values of the potential parameters we are using in this contribution.…”

Section: Structural Variations Along Isobarsmentioning

confidence: 99%

Competing ordered structures formed by particles with a regular tetrahedral patch decoration

Doppelbauer

Noya

Bianchi

et al. 2012

J. Phys.: Condens. Matter

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Abstract. We study the ordered equilibrium structures of patchy particles where the patches are located on the surface of the colloid such that they form a regular tetrahedron. Using optimization techniques based on ideas of evolutionary algorithms we identify possible candidate structures. We retain not only the energetically most favourable lattices but also include a few energetically less favourable particle arrangements (i.e., local minima on the enthalpy landscape). Using suitably developed Monte Carlo based simulations techniques in an NPT ensemble we evaluate the thermodynamic properties of these candidate structures along selected isobars and isotherms and identify thereby the respective ranges of stability. We demonstrate on a quantitative level that the equilibrium structures at a given state point result from a delicate compromise between entropy, energy (i.e., the lattice sum) and packing.

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“…A particle with tetrahedral arrangement of patches is thought to be a natural building block that would favor local tetrahedral arrangement, consistent with a diamond lattice. However, both Monte Carlo (MC) and Molecular Dynamics (MD) simulations of this system reveal serious fundamental limitations of such an approach [4,[14][15][16][17]. First, there are two forms of the diamond lattices: cubic diamond (CD) and hexagonal diamond (HD), both having local tetrahedral arrangement, as shown in Figure 1.…”

Section: Introductionmentioning

confidence: 99%

Layer-by-layer assembly of patchy particles as a route to nontrivial structures

Patra

Tkachenko

2017

Phys. Rev. E

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We propose a new strategy for robust high-quality self-assembly of non-trivial periodic structures out of patchy particles, and investigate it with Brownian Dynamics (BD) simulations. Its first element is the use of specific patch-patch and shell-shell interactions between the particles, that can be implemented through differential functionalization of patched and shell regions with specific DNA strands.The other key element of our approach is the use of layer-by-layer protocol that allows to avoid a formations of undesired random aggregates. As an example, we design and self-assemble "in silico" a version of a Double Diamond (DD) lattice in which four particle types are arranged into BCC crystal made of four FCC sublattices. The lattice can be further converted to Cubic Diamond (CD) by selective removal of the particles of certain types. Our results demonstrate that by combining the directionality, selectivity of interactions and the layer-by-layer protocol, a high quality robust self-assembly can be achieved. * oleksiyt@bnl.gov 2

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Phase diagram of a tetrahedral patchy particle model for different interaction ranges

Cited by 127 publications

References 42 publications

Liquids more stable than crystals in particles with limited valence and flexible bonds

Liquids more stable than crystals in particles with limited valence and flexible bonds

Competing ordered structures formed by particles with a regular tetrahedral patch decoration

Layer-by-layer assembly of patchy particles as a route to nontrivial structures

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